Given the coordinate matrix of x relative to a (nonstandard) basis 8 for R, find the coordinate matrix of x relative to the standard basis B-((3,-1), (0, 1)}, [x]s-

Need only a handwritten solution only (not a typed one).

Consider the bases v₁ = (1,0)¹, v₂ = (0, 1) and v₁ = (2, 1), v₂ = (1,3)¹ of R². The transition matrix from the basis {V₁, V₂} to the basis {v₁, v₂} is

|X= 3 -2 -2 2 ဦး + 0 1 + --L 1 Find a Basis for Column B of this Matrix

C: Let T be the linear operator associated in the standard basis B of F2 with the matrix 2 - [44] - 1 Let B' be the basis ((2, -1), (2, 1)) M = b) Using eachof these three matrices find the dimension of the range of T (you must check that the dimension is the same with all the matrices)